"Positional arguments" error in script
The functions assigned to bpy.app.handlers need to accept one parameter, even if they don't use it. While you can ignore the scene parameter I would suggest using it, rather than directly accessing global data (not that you are making use of the object variable you set).

import bpy

def object_update(scn):
    object = scn.objects['Cube']
    bpy.ops.object.explode_refresh(modifier="Explode")

bpy.app.handlers.render_pre.append(object_update)


Note that the explode_refresh operator will only work on the active object if it has an explode modifier named "Explode", so I'm not sure what you want to achieve will work, or that it is really necessary.